Law of the iterated logarithm for unstable Gaussian autoregressive models (Q2739700)

Let \(X_n\) be a stochastic process generated by the second order autoregression equation \(X_n=a_1X_{n-1}+a_2X_{n-2}+\gamma_n\), \(n\geq 1,\) where \(\gamma_n, n\geq 1,\) are i.i.d. standard Gaussian random variables. Let \(\lambda_1,\lambda_2\) be the roots of the equation \(\lambda^2-a_1\lambda-a_2=0\). The author investigates the behaviour of \(\lim\sup_{n\to\infty}n^{-1}\chi_n|x_n|,\) \(\chi_n=(n\ln\ln n)^{-1/2},n\geq 3,\) the case of an unstable autoregressive model \(|\lambda_2|\leq|\lambda_1|=1\).